cup (n.) Look up cup at Dictionary.com
Old English cuppe, from Late Latin cuppa "cup" (source of Italian coppa, Spanish copa, Old French coupe "cup"), from Latin cupa "tub, cask, tun, barrel," from PIE *keup- "a hollow" (cognates: Sanskrit kupah "hollow, pit, cave," Greek kype "a kind of ship," Old Church Slavonic kupu, Lithuanian kaupas).

The Late Latin word was borrowed throughout Germanic: Old Frisian kopp "cup, head," Middle Low German kopp "cup," Middle Dutch coppe, Dutch kopje "cup, head." German cognate Kopf now means exclusively "head" (compare French tête, from Latin testa "potsherd"). Meaning "part of a bra that holds a breast" is from 1938. [One's] cup of tea "what interests one" (1932), earlier used of persons (1908), the sense being "what is invigorating."
cup (v.) Look up cup at Dictionary.com
late 14c., "to draw blood by cupping," from cup (n.). Meaning "to form a cup" is from 1830. Related: Cupped; cupping.